A Poisson-Lie group is a Lie group \(G\)  endowed with a Poisson structure such that the multiplication is a Poisson map (see [1]}). If the Lie group \(G\)  is a vector space \(V\) , then \(V=\mathfrak {g}^*\)  is the dual space of a Lie algebra \(\mathfrak {g}\) , endowed with the Lie-Poisson structure. Poisson-Lie groups are in one-to-one correspondence with the so-called Lie bialgebras \((\mathfrak {g},\mathfrak {g}^*)\) , which are compatible pairs of Lie algebras in duality (for more details, see [2]}, [3]} or the recent survey paper [4]} and the references therein).
